[H]
Modified CoinPress [1]}

 Input: \(\hat{M} = (\hat{\mu }_1, \hdots , \hat{\mu }_k)\)  from a distribution with mean \(\mu \)  and covariance \(\Sigma \) ,
\(\tilde{\Sigma }\)  such that \(\hat{\Sigma } \preceq \tilde{\Sigma }\) ,
\(B_2(\tilde{\mu }_0,r_0)\)  containing \(\hat{\mu }\) ,
family of distributions \(Q_{\tilde{\mu }}(\cdot , \Sigma _{\hat{\mu }})\)  with heavier
tails than \(\hat{\mu }\) ,
\(t \in \mathbb {N}^+\) , \(\rho ^{\tilde{\mu }} > 0, \beta ^{\tilde{\mu }} > 0\)
